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kjetil b halvorsen
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FelB
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Distribution of stochastic integral

I would like to find the distributions of the following random variables:

$Z_k= \frac{1}{\pi} \int^{2\pi}_{0} cos(kt) dW_t$ $k=1,2,...$ and $(W_t)_{t\geq 0}$ is a Wiener process.

What is the distribution of $Z_1$, and $(Z_k) $?

I am new to stochastic calculus, I only know how to integrate a Wiener process wrt. an other Wiener process.

Can someone help me, how to do this?